Here's the first: donate a milk tooth to help an artist, Gina Czarnecki, build a four-foot-high magical fairytale palace out of resin encrusted with these unusual contributions. Why? (The first question all children ask). Well, it's partly art, darling, and partly to highlight some scientific issues which may not engage little ones – though they could trigger a torrent of further questions – but are interesting for the rest of us.

Part of the resin entrance to the palace, soon to be encrusted with milk teeth. guardian.co.uk

Here's what the festival organisers say:

Palaces will be exhibited at the Manchester Science Festival and is one of several pieces in the exhibition, which aims to explore the issue of waste body parts, such as fat from liposuction or bones from joint replacements, and how these could be used for stem cell regeneration. As more people donate their teeth, the Palace will grow over time like a coral reef, to form a stalagmite-like structure of crystal resin, encrusted in barnacle formations using baby teeth donated by children in the UK and around the world. To donate your milk teeth go online here.

As disposable body parts, milk teeth have particular potential for stem cell research. There is however, the knotty problem of the Tooth Fairy. Czarnecki has thought about this. She suggests:

the Palace is a magical place for a child to see their milk teeth but to avoid destroying the fairy side of things, why not leave a token or a letter created by the child on their pillow for the tooth fairy to collect, which means they can still receive money but the tooth is left behind to donate to the Palace.

She also wants to receive stories and drawings or find out what happens to children's milk teeth in different cultures. These will be part of a growing on line exhibition on the palace's website and some will form part of the exhibition as it tours nationally and overseas. As she says:

Teeth are one of the parts of the body we lose naturally, and their loss is a sign of growth and development rather than decay. Different cultures have varying traditions about where these teeth go, and what they are used for and I am interested in looking at how waste body parts such as teeth could play a new role in our own science-based culture. Your tooth will be carefully looked after by our own tooth fairy until it is ready to be added to the Palace, along with the thousands of other milk teeth donated.

I wish I had some to give. I have got my wisdom teeth in a box somewhere but they are hideous and large.

Finished flowering? Ready to count. Photograph: Vassil Donev/EPA

Idea two: the festival is making a final appeal to people to count the spirals in their sunflower heads as part of a truly vast experiment in honour of Alan Turing and his work on Fibonacci numbers and their relevance to computing and much else. The Fibonacci sequence, 1-1-2-3-5-8-13-21 etc, where each number is the sum of the two before it, appears regularly in the natural world, especially in sunflower spirals.The Guardian Northerner had a post about this earlier this year which attracted an interesting thread.

To check out the Manchester Sunflower appeal, which is approaching a vast tally of 12,000 flower heads, go to the website here Erinma Ochu, Project Manager of Turing's Sunflowers says:

Most sunflowers have now bloomed and are ready for counting, so please do join us to make every sunflower help towards the experiment. You can come along to one of our drop-in counting events or use the internet guide to help you count the spirals. We need enough sunflower data further the work of Alan Turing's investigation into Fibonacci numbers in nature and help to fill in the missing pieces of the puzzle that he left unsolved at his death.